German media reported Dortmund paid a fee of up to 10 million euros ($11 million), including bonuses, to sign the player.
A creative midfielder with an eye for goal, Gross joins the Champions League finalists after seven years with Brighton, having joined from German side FC Ingolstadt in 2017.
Gross, a Dortmund fan from childhood, said in a statement he "can’t wait to play alongside my new teammates".
Dortmund director Lars Ricken described Gross as a "top performer" who would add "solidity and flexibility" to the team.
In 228 Premier League appearances, Gross scored 30 goals and laid on 45 assists and helped Brighton qualify for European competition for the first time in their 122-year history after finishing sixth in the 2022-23 season.
Gross was named Brighton's player of the season twice: in his first season at the club in 2017-18 and last year in his final campaign.
The midfielder received his first Germany call-up at the age of 32 and was part of manager Julian Nagelsmann's 26-man squad at Euro 2024.
He has eight caps with one goal at international level.
Dortmund signed Gross after a poor domestic season in 2023-24.
Despite reaching the Champions League final, where they lost to Real Madrid at Wembley, Dortmund had a disappointing domestic campaign, finishing fifth in the league and eliminated at the last 16 of the German Cup.
This summer Dortmund have already signed striker Serhou Guirassy and defender Waldemar Anton, both from last season's surprise Bundesliga runners-up Stuttgart.